Chapter 7

For exercises 1-8, find the slope of the line that passes through the given points. $$ (9,15)(18,42) $$

For exercises 1-12, use prime factorization to find the least common denominator. $$ \frac{3}{4} ; \frac{5}{6} $$

Describe how to divide two fractions.

For exercises 1-66, simplify. $$ \frac{180}{420} $$

Explain why the relationship of the number of square feet of carpet that need to be vacuumed, \(x\), and the amount of time it takes to vacuum the carpet, \(y\), is a direct variation.

For exercises 1-10, (a) solve. (b) check. $$ \frac{3}{5} x-\frac{1}{4}=\frac{9}{10} $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ (8,14)(15,42) $$

For exercises 1-12, use prime factorization to find the least common denominator. $$ \frac{3}{8} ; \frac{5}{6} $$

For exercises \(1-4\), evaluate. $$ \frac{9}{50}+\frac{3}{50} $$

Describe how to multiply two fractions.

For exercises 1-66, simplify. $$ \frac{240}{540} $$

Explain why the relationship of the number of bags of leaves per hour that are raked, \(x\), and the hours it takes to rake a yard, \(y\), is an inverse variation.

For exercises 1-10, (a) solve. (b) check. $$ \frac{4}{9} p-\frac{1}{8}=\frac{25}{72} $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ \left(\frac{1}{9}, \frac{2}{15}\right)\left(\frac{5}{9}, \frac{11}{15}\right) $$

For exercises 1-12, use prime factorization to find the least common denominator. $$ \frac{5}{18 x} ; \frac{1}{30 x^{2}} $$

For exercises \(1-4\), evaluate. $$ \frac{12}{35}-\frac{2}{35} $$

For exercises \(3-6\), evaluate or simplify. $$ \frac{3}{20} \cdot \frac{2}{15} $$

For exercises 1-66, simplify. $$ \frac{48 a^{2} b^{3}}{56 a b} $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ \left(\frac{3}{8}, \frac{4}{9}\right)\left(\frac{7}{8}, \frac{8}{9}\right) $$

For exercises 1-12, use prime factorization to find the least common denominator. $$ \frac{7}{15 y} ; \frac{1}{24 y^{2}} $$

For exercises \(1-4\), evaluate. $$ \frac{16}{21}-\frac{4}{21} $$

For exercises \(3-6\), evaluate or simplify. $$ \frac{4}{15} \cdot \frac{5}{12} $$

For exercises 1-66, simplify. $$ \frac{54 c^{2} d^{5}}{72 c d} $$

The relationship of \(x\) and \(y\) is a direct variation. When \(x=2, y=6\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this direct variation. c. Find \(y\) when \(x=4\). d. Use slope-intercept graphing to graph this equation. e. Use the graph to find \(y\) when \(x=5\).

For exercises 1-10, (a) solve. (b) check. $$ \frac{4}{15} k+\frac{3}{4}=-2 $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ \left(\frac{3}{8}, \frac{2}{5}\right)\left(\frac{9}{16}, \frac{3}{4}\right) $$

For exercises \(5-48\), simplify. $$ \frac{2}{x+8}+\frac{8}{x+8} $$

For exercises 1-66, simplify. $$ \frac{90 n^{2} p^{8}}{42 n^{5} p^{6}} $$

For exercises 1-10, (a) solve. (b) check. $$ \frac{1}{6} w+\frac{23}{8}=-3 $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ \left(\frac{2}{3}, \frac{9}{10}\right)\left(\frac{5}{8}, \frac{11}{20}\right) $$

For exercises \(5-48\), simplify. $$ \frac{3}{x+5}+\frac{5}{x+5} $$

For exercises \(3-6\), evaluate or simplify. $$ \frac{3 x}{10} \cdot \frac{5}{24} $$

For exercises 1-66, simplify. $$ \frac{80 w^{3} z^{7}}{48 w^{9} z^{5}} $$

The relationship of \(x\) and \(y\) is a direct variation. When \(x=1, y=6\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this direct variation. c. Find \(y\) when \(x=4\), d. Use slope-intercept graphing to graph this equation. e. Use the graph to find \(y\) when \(x=2\).

For exercises 1-10, (a) solve. (b) check. $$ \frac{2}{3} x+\frac{3}{2}=\frac{1}{3} x+\frac{1}{6} $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ \left(\frac{3}{8},-\frac{1}{2}\right)\left(-\frac{5}{8},-\frac{5}{2}\right) $$

For exercises 1-12, use prime factorization to find the least common denominator. $$ \frac{2}{x^{2}-7 x} ; \frac{3}{3 x-21} $$

For exercises \(5-48\), simplify. $$ \frac{15}{x-9}-\frac{6}{x-9} $$

For exercises 1-66, simplify. $$ \frac{28 x y^{5}}{56 x y} $$

The relationship of \(x\) and \(y\) is a direct variation. When \(x=1, y=5\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this direct variation. c. Find \(y\) when \(x=2\). d. Use slope-intercept graphing to graph this equation. e. Use the graph to find \(y\) when \(x=3\).

For exercises 1-10, (a) solve. (b) check. $$ \frac{2}{9} x+\frac{5}{3}=\frac{5}{9} x+\frac{7}{3} $$

For exercises 1-8, find the slope of the line that passes through the given points. $$ \left(\frac{5}{9},-\frac{1}{3}\right)\left(-\frac{7}{9},-\frac{5}{3}\right) $$

For exercises \(5-48\), simplify. $$ \frac{14}{x-5}-\frac{9}{x-5} $$

For exercises 7-32, simplify. $$ \left(\frac{8}{5 w+10}\right)\left(\frac{5}{24}\right) $$

For exercises 1-66, simplify. $$ \frac{27 h k^{4}}{54 h k} $$

The relationship of the amount of weed killer concentrate, \(x\), and the amount of mixed weed killer spray, \(y\), is a direct variation. A gardener uses \(2 \mathrm{oz}\) of concentrate to make 1 gal of weed killer spray. a. Find the constant of proportionality, \(k\). Include the units of measurement. b. Write an equation that represents this relationship. c. Find the amount of mixed weed killer spray that can be made with \(8 \mathrm{oz}\) of concentrate. d. Use slope-intercept graphing to graph this equation. e. Use the graph to find the amount of mixed weed killer spray that can be made with \(6 \mathrm{oz}\) of concentrate.

For exercises \(9-24\), evaluate or simplify. $$ \frac{\frac{2}{3}}{\frac{5}{6}} $$

For exercises 1-12, use prime factorization to find the least common denominator. $$ \frac{1}{50 x^{2} y} ; \frac{1}{35 x y^{3} z} $$

For exercises 1-66, simplify. $$ \frac{2 x-8}{10} $$

The relationship of the amount of salad dressing, \(x\), and the amount of sodium in the dressing, \(y\), is a direct variation. Six servings of dressing contain \(1800 \mathrm{mg}\) of sodium. a. Find the constant of proportionality, \(k\). Include the units of measurement. b. Write an equation that represents this relationship. c. Find the amount of sodium in a bottle that contains 16 servings of salad dressing. d. Use slope-intercept graphing to graph this equation. e. Use the graph to find the amount of sodium in 3 servings of salad dressing.